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Simplifying 0 = 3h2 + 32h + -3584 Reorder the terms: 0 = -3584 + 32h + 3h2 Solving 0 = -3584 + 32h + 3h2 Solving for variable 'h'. Combine like terms: 0 + 3584 = 3584 3584 + -32h + -3h2 = -3584 + 32h + 3h2 + 3584 + -32h + -3h2 Reorder the terms: 3584 + -32h + -3h2 = -3584 + 3584 + 32h + -32h + 3h2 + -3h2 Combine like terms: -3584 + 3584 = 0 3584 + -32h + -3h2 = 0 + 32h + -32h + 3h2 + -3h2 3584 + -32h + -3h2 = 32h + -32h + 3h2 + -3h2 Combine like terms: 32h + -32h = 0 3584 + -32h + -3h2 = 0 + 3h2 + -3h2 3584 + -32h + -3h2 = 3h2 + -3h2 Combine like terms: 3h2 + -3h2 = 0 3584 + -32h + -3h2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -1194.666667 + 10.66666667h + h2 = 0 Move the constant term to the right: Add '1194.666667' to each side of the equation. -1194.666667 + 10.66666667h + 1194.666667 + h2 = 0 + 1194.666667 Reorder the terms: -1194.666667 + 1194.666667 + 10.66666667h + h2 = 0 + 1194.666667 Combine like terms: -1194.666667 + 1194.666667 = 0.000000 0.000000 + 10.66666667h + h2 = 0 + 1194.666667 10.66666667h + h2 = 0 + 1194.666667 Combine like terms: 0 + 1194.666667 = 1194.666667 10.66666667h + h2 = 1194.666667 The h term is 10.66666667h. Take half its coefficient (5.333333335). Square it (28.44444446) and add it to both sides. Add '28.44444446' to each side of the equation. 10.66666667h + 28.44444446 + h2 = 1194.666667 + 28.44444446 Reorder the terms: 28.44444446 + 10.66666667h + h2 = 1194.666667 + 28.44444446 Combine like terms: 1194.666667 + 28.44444446 = 1223.11111146 28.44444446 + 10.66666667h + h2 = 1223.11111146 Factor a perfect square on the left side: (h + 5.333333335)(h + 5.333333335) = 1223.11111146 Calculate the square root of the right side: 34.973005468 Break this problem into two subproblems by setting (h + 5.333333335) equal to 34.973005468 and -34.973005468.Subproblem 1
h + 5.333333335 = 34.973005468 Simplifying h + 5.333333335 = 34.973005468 Reorder the terms: 5.333333335 + h = 34.973005468 Solving 5.333333335 + h = 34.973005468 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + h = 34.973005468 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + h = 34.973005468 + -5.333333335 h = 34.973005468 + -5.333333335 Combine like terms: 34.973005468 + -5.333333335 = 29.639672133 h = 29.639672133 Simplifying h = 29.639672133Subproblem 2
h + 5.333333335 = -34.973005468 Simplifying h + 5.333333335 = -34.973005468 Reorder the terms: 5.333333335 + h = -34.973005468 Solving 5.333333335 + h = -34.973005468 Solving for variable 'h'. Move all terms containing h to the left, all other terms to the right. Add '-5.333333335' to each side of the equation. 5.333333335 + -5.333333335 + h = -34.973005468 + -5.333333335 Combine like terms: 5.333333335 + -5.333333335 = 0.000000000 0.000000000 + h = -34.973005468 + -5.333333335 h = -34.973005468 + -5.333333335 Combine like terms: -34.973005468 + -5.333333335 = -40.306338803 h = -40.306338803 Simplifying h = -40.306338803Solution
The solution to the problem is based on the solutions from the subproblems. h = {29.639672133, -40.306338803}
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